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Gaussian function: Revision history


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  • curprev 21:0721:07, 21 August 2021Zanderteller talk contribsm 27,911 bytes +18 The existing statement was this: "The nth derivative of the Gaussian is the Gaussian function itself multiplied by the nth Hermite polynomial, up to scale." This statement is not generally true (or, at best, is easily misunderstood). For example, the 2nd derivative of the Gaussian function (up to scale) is not (x^2 - 1) times the Gaussian -- it is (x^2 - sigma^2) times the Gaussian. The statement becomes true when sigma is 1 (i.e., with unit variance). undo

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